What is the ruling of Islamic law on paying a sum of money as a "bribe" to obtain social housing, or giving it as a "gift," especially since the person is compelled to do so, and is it permissible not to fulfill this promise?

Bribery is of two types: forbidden if it leads to validating falsehood or invalidating truth, and its doer is cursed. It is permissible for the giver and forbidden for the receiver if it is a means to obtain a right or ward off harm. Therefore, there is no harm in paying money to obtain deserved housing if there is no other way, and the receiver bears the sin of the bribe.